Defense Secretary Ash Carter and Joint Chiefs of Staff Chairman Gen. Joseph Dunford held a press briefing Friday to announce the killing of ISIL's finance chief and to highlight a series of recent blows to the group in Iraq and Syria. | Getty

Obama team pushes back: We're beating the terrorists

'The momentum of this campaign is now clearly on our side,' Pentagon chief Ash Carter says.

The Obama administration, under withering criticism on Capitol Hill and on the campaign trail, on Friday deployed itstop architects of the war against the Islamic State with the strongest claims yet that severe damage is being inflicted on the terrorist network that has claimed responsibility for the Brussels bombings.

In a rejoinder to days of verbal assaults from multiple political quarters, Defense Secretary Ash Carter and Joint Chiefs Chairman Gen. Joe Dunford held a news briefing at the Pentagon to announce the killing of the group's finance chief, Haji Imam, and to highlight a series of recent blows to the group in Iraq and Syria.

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“The momentum of this campaign is now clearly on our side," Carter declared.

He said that the finance chief, one of several top operatives killed in recent days, played a role in funding and plotting attacks and his removal "will hamper the organization’s ability to conduct operations inside and outside of Syria."

"We are systematically eliminating ISIL’s cabinet," he added, using the acronym for the Islamic State of Iraq and the Levant.

There was a similar message Friday from Secretary of State John Kerry, who has unsuccessfully sought an end to the Syrian civil war.

Using the Arabic acronym for the group, he told CBS News that "40 percent of the territory that Daesh held has been taken back. Their leadership is being taken apart, their revenue is being cut. ... What you're seeing [in Europe] are desperation, lash-out events."

The upbeat assessments came after days of political heat over the progress of the fight.

Republican presidential contenders Donald Trump and Sen. Ted Cruz of Texas have blasted President Barack Obama for continuing his historic trip to Cuba in the aftermath of the Belgium attacks that killed 31 people, including at least two Americans, and injured hundreds more.

Even as Carter and Dunford spoke, Republican members of Congress were knocking the administration for delivering a seven-page campaign plan for defeating the Islamic State — a plan that arrived a month late and replayed many of the same talking points that hawks have long decried as insufficient.

In a statement Friday, Sen. Lindsey Graham, a South Carolina Republican and senior member of the Armed Services Committee, hailed the death of the finance chief but said "these type operations are necessary to disrupt ISIL, but they are no substitute for a sustained ground campaign which ultimately destroys the organization.

"Raids like these help, but at the end of the day it will take an army to defeat an army," Graham added.

But Carter and Dunford's appearance was clearly an attempt to press the administration's view that the group is reeling from the 17-month air campaign in Iraq and Syria and a spate of recent victories spearheaded by Iraqi security forces to dislodge the group from key population centers in Western Iraq.

One of the more hawkish members of Obama's national security team, Carter portrayed the special forces raid inside Syria that killed the finance chief as a result of the recent strides made by the U.S.-led military campaign.

Haji Imam was a longtime U.S. adversary who Carter said had worked under Abu Musab al-Zarqawi, the notorious terrorist commander who wreaked havoc across Iraq before he was killed in a U.S. airstrike in 2006.

Carter said he was one of several “key terrorists” killed this week.

"Leaders can be replaced. However these leaders have been around for a long time. They are senior. They are experienced, and so eliminating them is an important objective and achieves important results," Carter said. “We’ve learned a great deal, and we continue to learn about who is who in ISIL so we can kill them, about how they get their finances so we can dry that up."

He could not say whether there was a direct link more broadly between top ISIL officials and terrorist attacks in Europe in the past six months but stressed that defeating the group in Iraq and Syria will be tantamount to draining its attraction elsewhere.

“Even if it’s just inspiration, it still takes you back to Iraq and Syria and the need to eliminate the sources of that inspiration," Carter said. "The idea that there can be this Islamic State based upon this ideology, with a capital in Raqqa [in Syria] — we’re going to eliminate that image.”

The Pentagon chief again asserted that Iraqi security forces are laying the groundwork for a major — and high-risk — assault on Mosul, Iraq's second largest city and a major stronghold of the group.

"The forces that we’re working with on the ground in both Iraq and Syria continue to gather strength because our strategic approach for the retaking of territory is to help local forces to do so.”

The administration has also taken heat after it was revealed earlier this week the U.S. troop presence in Iraq is larger than previously believed — exceeding the administration’s 3,870-troop cap because troops there on temporary assignments are not counted.

The U.S. Marine whose death at a fire base in Iraq was announced last weekend was there on temporary assignment, officials acknowledged.

Dunford on Friday insisted the methods for counting troops involved in the campaign lined up with past practices.

“The accounting of our people has been consistent,” he told reporters Friday. “We're not denying that there's been more people than 3,800.”

But the general also predicted that the U.S. troop presence will likely grow.

"The secretary and I both believe that there will be an increase in U.S. forces in Iraq in coming weeks, but that decision hasn't been made," Dunford said. "We have a series of recommendations that we will be discussing with the president in the coming weeks to further enable our support for the Iraqi security forces," the president's top military adviser added.

Thomas Sanderson, who directs the Transnational Threats Project at the Center for Strategic and International Studies, said the recent battlefield successes are important but will not solve the underlying problems driving Muslims to extremism, such as the Syrian civil war, a lack of jobs and education, and exclusion of Sunni Arabs by the Iraqi government.

“Huge fundamental underlying problems are not fixed," Sanderson said. "These tactical advances are good but perishable in their impact on broader society and the broader battle.”

Even the steady progress on the battlefield won't guarantee the group stays defeated, Carter has acknowledged in recent days.

"Not only do we need to defeat ISIL," Carter told POLITICO in an interview last week, "we need to keep them defeated, and we know what that means. It means somebody has to govern these places after the defeat in a way that the people can accept and is decent and not barbaric."